Blender game character not responding to game logic
In one of the files you sent, RigRichardMaleGame.blend, you did several things wrong, the two most significant being that you moved the metarig away from the generated rig instead of just hiding it. See #4 here.

That next thing you did wrong was remove the Armature modifier from the base mesh, this is what links the mesh to the rig. Your animations will playback in the viewport as these have already been keyframed but the game engine's Action Actuator needs this to know what mesh to associate the selected action with. The action was playing in the game engine, the mesh just wasn't being updated (hence why it went back to the default pose).

So to fix, just add an Armature modifier to the mesh and select the hidden rig which is the proper (unmodified) one, (metarig).

NB: I would highly suggest not revisiting that scene at all. It's very botched (in terms of scene settings, scale and organization) and would no doubt lead to a plethora of further errors down the line. I would instead recommend appending out the base mesh, rigging it again (a matter of minutes using Rigify) and then reanimating and making sure this time to not remove the armature modifier or mess too much with the generated rig.